Properties

Label 280.6.a.j.1.5
Level $280$
Weight $6$
Character 280.1
Self dual yes
Analytic conductor $44.907$
Analytic rank $0$
Dimension $5$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 280.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(44.9074695476\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: \(\mathbb{Q}[x]/(x^{5} - \cdots)\)
Defining polynomial: \(x^{5} - 1151 x^{3} - 5642 x^{2} + 193596 x + 1258056\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(-27.3320\) of defining polynomial
Character \(\chi\) \(=\) 280.1

$q$-expansion

\(f(q)\) \(=\) \(q+30.3320 q^{3} +25.0000 q^{5} +49.0000 q^{7} +677.031 q^{9} +O(q^{10})\) \(q+30.3320 q^{3} +25.0000 q^{5} +49.0000 q^{7} +677.031 q^{9} +604.346 q^{11} +383.964 q^{13} +758.300 q^{15} -791.640 q^{17} -2078.78 q^{19} +1486.27 q^{21} -2523.45 q^{23} +625.000 q^{25} +13165.0 q^{27} +372.040 q^{29} -2484.87 q^{31} +18331.0 q^{33} +1225.00 q^{35} -6552.46 q^{37} +11646.4 q^{39} -16194.7 q^{41} +15433.1 q^{43} +16925.8 q^{45} +22278.8 q^{47} +2401.00 q^{49} -24012.0 q^{51} -26272.4 q^{53} +15108.6 q^{55} -63053.6 q^{57} +39869.1 q^{59} +5893.86 q^{61} +33174.5 q^{63} +9599.11 q^{65} -32074.7 q^{67} -76541.3 q^{69} -57992.0 q^{71} +39480.1 q^{73} +18957.5 q^{75} +29612.9 q^{77} -8987.90 q^{79} +234804. q^{81} -52523.4 q^{83} -19791.0 q^{85} +11284.7 q^{87} +52068.7 q^{89} +18814.3 q^{91} -75371.1 q^{93} -51969.5 q^{95} +14928.3 q^{97} +409161. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q + 15 q^{3} + 125 q^{5} + 245 q^{7} + 1132 q^{9} + O(q^{10}) \) \( 5 q + 15 q^{3} + 125 q^{5} + 245 q^{7} + 1132 q^{9} + 281 q^{11} + 909 q^{13} + 375 q^{15} + 1495 q^{17} - 422 q^{19} + 735 q^{21} - 62 q^{23} + 3125 q^{25} - 3363 q^{27} - 2047 q^{29} + 1636 q^{31} + 19181 q^{33} + 6125 q^{35} - 10358 q^{37} + 15685 q^{39} + 6424 q^{41} + 28306 q^{43} + 28300 q^{45} + 20955 q^{47} + 12005 q^{49} - 23577 q^{51} + 43748 q^{53} + 7025 q^{55} + 13690 q^{57} + 45788 q^{59} + 50432 q^{61} + 55468 q^{63} + 22725 q^{65} + 40712 q^{67} + 35050 q^{69} - 3096 q^{71} + 135438 q^{73} + 9375 q^{75} + 13769 q^{77} + 13191 q^{79} + 381101 q^{81} + 35108 q^{83} + 37375 q^{85} + 297289 q^{87} + 213772 q^{89} + 44541 q^{91} + 134244 q^{93} - 10550 q^{95} + 10659 q^{97} + 39462 q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 30.3320 1.94580 0.972900 0.231227i \(-0.0742739\pi\)
0.972900 + 0.231227i \(0.0742739\pi\)
\(4\) 0 0
\(5\) 25.0000 0.447214
\(6\) 0 0
\(7\) 49.0000 0.377964
\(8\) 0 0
\(9\) 677.031 2.78614
\(10\) 0 0
\(11\) 604.346 1.50593 0.752963 0.658063i \(-0.228624\pi\)
0.752963 + 0.658063i \(0.228624\pi\)
\(12\) 0 0
\(13\) 383.964 0.630133 0.315067 0.949070i \(-0.397973\pi\)
0.315067 + 0.949070i \(0.397973\pi\)
\(14\) 0 0
\(15\) 758.300 0.870188
\(16\) 0 0
\(17\) −791.640 −0.664363 −0.332181 0.943216i \(-0.607785\pi\)
−0.332181 + 0.943216i \(0.607785\pi\)
\(18\) 0 0
\(19\) −2078.78 −1.32107 −0.660533 0.750797i \(-0.729670\pi\)
−0.660533 + 0.750797i \(0.729670\pi\)
\(20\) 0 0
\(21\) 1486.27 0.735443
\(22\) 0 0
\(23\) −2523.45 −0.994660 −0.497330 0.867561i \(-0.665686\pi\)
−0.497330 + 0.867561i \(0.665686\pi\)
\(24\) 0 0
\(25\) 625.000 0.200000
\(26\) 0 0
\(27\) 13165.0 3.47546
\(28\) 0 0
\(29\) 372.040 0.0821475 0.0410737 0.999156i \(-0.486922\pi\)
0.0410737 + 0.999156i \(0.486922\pi\)
\(30\) 0 0
\(31\) −2484.87 −0.464408 −0.232204 0.972667i \(-0.574594\pi\)
−0.232204 + 0.972667i \(0.574594\pi\)
\(32\) 0 0
\(33\) 18331.0 2.93023
\(34\) 0 0
\(35\) 1225.00 0.169031
\(36\) 0 0
\(37\) −6552.46 −0.786865 −0.393433 0.919354i \(-0.628712\pi\)
−0.393433 + 0.919354i \(0.628712\pi\)
\(38\) 0 0
\(39\) 11646.4 1.22611
\(40\) 0 0
\(41\) −16194.7 −1.50458 −0.752289 0.658834i \(-0.771050\pi\)
−0.752289 + 0.658834i \(0.771050\pi\)
\(42\) 0 0
\(43\) 15433.1 1.27287 0.636433 0.771332i \(-0.280409\pi\)
0.636433 + 0.771332i \(0.280409\pi\)
\(44\) 0 0
\(45\) 16925.8 1.24600
\(46\) 0 0
\(47\) 22278.8 1.47112 0.735559 0.677460i \(-0.236919\pi\)
0.735559 + 0.677460i \(0.236919\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) −24012.0 −1.29272
\(52\) 0 0
\(53\) −26272.4 −1.28472 −0.642362 0.766401i \(-0.722046\pi\)
−0.642362 + 0.766401i \(0.722046\pi\)
\(54\) 0 0
\(55\) 15108.6 0.673471
\(56\) 0 0
\(57\) −63053.6 −2.57053
\(58\) 0 0
\(59\) 39869.1 1.49110 0.745549 0.666451i \(-0.232187\pi\)
0.745549 + 0.666451i \(0.232187\pi\)
\(60\) 0 0
\(61\) 5893.86 0.202804 0.101402 0.994846i \(-0.467667\pi\)
0.101402 + 0.994846i \(0.467667\pi\)
\(62\) 0 0
\(63\) 33174.5 1.05306
\(64\) 0 0
\(65\) 9599.11 0.281804
\(66\) 0 0
\(67\) −32074.7 −0.872922 −0.436461 0.899723i \(-0.643768\pi\)
−0.436461 + 0.899723i \(0.643768\pi\)
\(68\) 0 0
\(69\) −76541.3 −1.93541
\(70\) 0 0
\(71\) −57992.0 −1.36528 −0.682641 0.730754i \(-0.739169\pi\)
−0.682641 + 0.730754i \(0.739169\pi\)
\(72\) 0 0
\(73\) 39480.1 0.867103 0.433552 0.901129i \(-0.357260\pi\)
0.433552 + 0.901129i \(0.357260\pi\)
\(74\) 0 0
\(75\) 18957.5 0.389160
\(76\) 0 0
\(77\) 29612.9 0.569187
\(78\) 0 0
\(79\) −8987.90 −0.162028 −0.0810141 0.996713i \(-0.525816\pi\)
−0.0810141 + 0.996713i \(0.525816\pi\)
\(80\) 0 0
\(81\) 234804. 3.97642
\(82\) 0 0
\(83\) −52523.4 −0.836870 −0.418435 0.908247i \(-0.637421\pi\)
−0.418435 + 0.908247i \(0.637421\pi\)
\(84\) 0 0
\(85\) −19791.0 −0.297112
\(86\) 0 0
\(87\) 11284.7 0.159843
\(88\) 0 0
\(89\) 52068.7 0.696790 0.348395 0.937348i \(-0.386727\pi\)
0.348395 + 0.937348i \(0.386727\pi\)
\(90\) 0 0
\(91\) 18814.3 0.238168
\(92\) 0 0
\(93\) −75371.1 −0.903645
\(94\) 0 0
\(95\) −51969.5 −0.590799
\(96\) 0 0
\(97\) 14928.3 0.161094 0.0805472 0.996751i \(-0.474333\pi\)
0.0805472 + 0.996751i \(0.474333\pi\)
\(98\) 0 0
\(99\) 409161. 4.19572
\(100\) 0 0
\(101\) −137155. −1.33785 −0.668927 0.743328i \(-0.733246\pi\)
−0.668927 + 0.743328i \(0.733246\pi\)
\(102\) 0 0
\(103\) −112201. −1.04208 −0.521041 0.853532i \(-0.674456\pi\)
−0.521041 + 0.853532i \(0.674456\pi\)
\(104\) 0 0
\(105\) 37156.7 0.328900
\(106\) 0 0
\(107\) 195834. 1.65360 0.826798 0.562499i \(-0.190160\pi\)
0.826798 + 0.562499i \(0.190160\pi\)
\(108\) 0 0
\(109\) 220762. 1.77974 0.889872 0.456210i \(-0.150793\pi\)
0.889872 + 0.456210i \(0.150793\pi\)
\(110\) 0 0
\(111\) −198749. −1.53108
\(112\) 0 0
\(113\) −51394.7 −0.378636 −0.189318 0.981916i \(-0.560628\pi\)
−0.189318 + 0.981916i \(0.560628\pi\)
\(114\) 0 0
\(115\) −63086.2 −0.444826
\(116\) 0 0
\(117\) 259956. 1.75564
\(118\) 0 0
\(119\) −38790.4 −0.251106
\(120\) 0 0
\(121\) 204183. 1.26781
\(122\) 0 0
\(123\) −491219. −2.92761
\(124\) 0 0
\(125\) 15625.0 0.0894427
\(126\) 0 0
\(127\) −35496.6 −0.195289 −0.0976445 0.995221i \(-0.531131\pi\)
−0.0976445 + 0.995221i \(0.531131\pi\)
\(128\) 0 0
\(129\) 468118. 2.47674
\(130\) 0 0
\(131\) 130196. 0.662857 0.331428 0.943480i \(-0.392469\pi\)
0.331428 + 0.943480i \(0.392469\pi\)
\(132\) 0 0
\(133\) −101860. −0.499316
\(134\) 0 0
\(135\) 329126. 1.55427
\(136\) 0 0
\(137\) −260457. −1.18559 −0.592795 0.805353i \(-0.701976\pi\)
−0.592795 + 0.805353i \(0.701976\pi\)
\(138\) 0 0
\(139\) 91256.3 0.400614 0.200307 0.979733i \(-0.435806\pi\)
0.200307 + 0.979733i \(0.435806\pi\)
\(140\) 0 0
\(141\) 675762. 2.86250
\(142\) 0 0
\(143\) 232047. 0.948935
\(144\) 0 0
\(145\) 9300.99 0.0367375
\(146\) 0 0
\(147\) 72827.2 0.277971
\(148\) 0 0
\(149\) 450638. 1.66289 0.831443 0.555610i \(-0.187515\pi\)
0.831443 + 0.555610i \(0.187515\pi\)
\(150\) 0 0
\(151\) −322713. −1.15179 −0.575896 0.817523i \(-0.695347\pi\)
−0.575896 + 0.817523i \(0.695347\pi\)
\(152\) 0 0
\(153\) −535965. −1.85101
\(154\) 0 0
\(155\) −62121.8 −0.207690
\(156\) 0 0
\(157\) −106359. −0.344371 −0.172186 0.985065i \(-0.555083\pi\)
−0.172186 + 0.985065i \(0.555083\pi\)
\(158\) 0 0
\(159\) −796895. −2.49982
\(160\) 0 0
\(161\) −123649. −0.375946
\(162\) 0 0
\(163\) −134910. −0.397719 −0.198860 0.980028i \(-0.563724\pi\)
−0.198860 + 0.980028i \(0.563724\pi\)
\(164\) 0 0
\(165\) 458276. 1.31044
\(166\) 0 0
\(167\) −232478. −0.645047 −0.322523 0.946561i \(-0.604531\pi\)
−0.322523 + 0.946561i \(0.604531\pi\)
\(168\) 0 0
\(169\) −223864. −0.602932
\(170\) 0 0
\(171\) −1.40740e6 −3.68067
\(172\) 0 0
\(173\) −150150. −0.381427 −0.190713 0.981646i \(-0.561080\pi\)
−0.190713 + 0.981646i \(0.561080\pi\)
\(174\) 0 0
\(175\) 30625.0 0.0755929
\(176\) 0 0
\(177\) 1.20931e6 2.90138
\(178\) 0 0
\(179\) −537663. −1.25423 −0.627115 0.778926i \(-0.715765\pi\)
−0.627115 + 0.778926i \(0.715765\pi\)
\(180\) 0 0
\(181\) −474105. −1.07567 −0.537834 0.843051i \(-0.680757\pi\)
−0.537834 + 0.843051i \(0.680757\pi\)
\(182\) 0 0
\(183\) 178773. 0.394615
\(184\) 0 0
\(185\) −163812. −0.351897
\(186\) 0 0
\(187\) −478424. −1.00048
\(188\) 0 0
\(189\) 645087. 1.31360
\(190\) 0 0
\(191\) −991261. −1.96610 −0.983048 0.183348i \(-0.941306\pi\)
−0.983048 + 0.183348i \(0.941306\pi\)
\(192\) 0 0
\(193\) −398252. −0.769598 −0.384799 0.923000i \(-0.625729\pi\)
−0.384799 + 0.923000i \(0.625729\pi\)
\(194\) 0 0
\(195\) 291160. 0.548335
\(196\) 0 0
\(197\) 424086. 0.778553 0.389277 0.921121i \(-0.372725\pi\)
0.389277 + 0.921121i \(0.372725\pi\)
\(198\) 0 0
\(199\) −178201. −0.318991 −0.159495 0.987199i \(-0.550987\pi\)
−0.159495 + 0.987199i \(0.550987\pi\)
\(200\) 0 0
\(201\) −972890. −1.69853
\(202\) 0 0
\(203\) 18229.9 0.0310488
\(204\) 0 0
\(205\) −404869. −0.672867
\(206\) 0 0
\(207\) −1.70845e6 −2.77126
\(208\) 0 0
\(209\) −1.25630e6 −1.98943
\(210\) 0 0
\(211\) 837166. 1.29451 0.647255 0.762273i \(-0.275917\pi\)
0.647255 + 0.762273i \(0.275917\pi\)
\(212\) 0 0
\(213\) −1.75901e6 −2.65656
\(214\) 0 0
\(215\) 385828. 0.569243
\(216\) 0 0
\(217\) −121759. −0.175530
\(218\) 0 0
\(219\) 1.19751e6 1.68721
\(220\) 0 0
\(221\) −303961. −0.418637
\(222\) 0 0
\(223\) −545816. −0.734995 −0.367497 0.930025i \(-0.619785\pi\)
−0.367497 + 0.930025i \(0.619785\pi\)
\(224\) 0 0
\(225\) 423145. 0.557227
\(226\) 0 0
\(227\) 1.12689e6 1.45151 0.725753 0.687956i \(-0.241492\pi\)
0.725753 + 0.687956i \(0.241492\pi\)
\(228\) 0 0
\(229\) 1.35322e6 1.70522 0.852610 0.522547i \(-0.175018\pi\)
0.852610 + 0.522547i \(0.175018\pi\)
\(230\) 0 0
\(231\) 898220. 1.10752
\(232\) 0 0
\(233\) 1.17172e6 1.41395 0.706975 0.707238i \(-0.250059\pi\)
0.706975 + 0.707238i \(0.250059\pi\)
\(234\) 0 0
\(235\) 556971. 0.657904
\(236\) 0 0
\(237\) −272621. −0.315274
\(238\) 0 0
\(239\) −1.63077e6 −1.84671 −0.923355 0.383946i \(-0.874565\pi\)
−0.923355 + 0.383946i \(0.874565\pi\)
\(240\) 0 0
\(241\) −459984. −0.510153 −0.255076 0.966921i \(-0.582101\pi\)
−0.255076 + 0.966921i \(0.582101\pi\)
\(242\) 0 0
\(243\) 3.92296e6 4.26185
\(244\) 0 0
\(245\) 60025.0 0.0638877
\(246\) 0 0
\(247\) −798178. −0.832448
\(248\) 0 0
\(249\) −1.59314e6 −1.62838
\(250\) 0 0
\(251\) −26214.6 −0.0262639 −0.0131319 0.999914i \(-0.504180\pi\)
−0.0131319 + 0.999914i \(0.504180\pi\)
\(252\) 0 0
\(253\) −1.52504e6 −1.49789
\(254\) 0 0
\(255\) −600301. −0.578121
\(256\) 0 0
\(257\) −1.10412e6 −1.04275 −0.521377 0.853326i \(-0.674582\pi\)
−0.521377 + 0.853326i \(0.674582\pi\)
\(258\) 0 0
\(259\) −321071. −0.297407
\(260\) 0 0
\(261\) 251882. 0.228874
\(262\) 0 0
\(263\) 219876. 0.196015 0.0980074 0.995186i \(-0.468753\pi\)
0.0980074 + 0.995186i \(0.468753\pi\)
\(264\) 0 0
\(265\) −656810. −0.574546
\(266\) 0 0
\(267\) 1.57935e6 1.35581
\(268\) 0 0
\(269\) 1.85329e6 1.56157 0.780786 0.624799i \(-0.214819\pi\)
0.780786 + 0.624799i \(0.214819\pi\)
\(270\) 0 0
\(271\) 1.70884e6 1.41344 0.706722 0.707492i \(-0.250173\pi\)
0.706722 + 0.707492i \(0.250173\pi\)
\(272\) 0 0
\(273\) 570674. 0.463427
\(274\) 0 0
\(275\) 377716. 0.301185
\(276\) 0 0
\(277\) 188853. 0.147885 0.0739424 0.997263i \(-0.476442\pi\)
0.0739424 + 0.997263i \(0.476442\pi\)
\(278\) 0 0
\(279\) −1.68233e6 −1.29390
\(280\) 0 0
\(281\) 1.77467e6 1.34076 0.670380 0.742018i \(-0.266131\pi\)
0.670380 + 0.742018i \(0.266131\pi\)
\(282\) 0 0
\(283\) 472156. 0.350445 0.175222 0.984529i \(-0.443936\pi\)
0.175222 + 0.984529i \(0.443936\pi\)
\(284\) 0 0
\(285\) −1.57634e6 −1.14958
\(286\) 0 0
\(287\) −793543. −0.568677
\(288\) 0 0
\(289\) −793163. −0.558622
\(290\) 0 0
\(291\) 452805. 0.313458
\(292\) 0 0
\(293\) −642119. −0.436965 −0.218482 0.975841i \(-0.570111\pi\)
−0.218482 + 0.975841i \(0.570111\pi\)
\(294\) 0 0
\(295\) 996727. 0.666839
\(296\) 0 0
\(297\) 7.95624e6 5.23379
\(298\) 0 0
\(299\) −968914. −0.626769
\(300\) 0 0
\(301\) 756223. 0.481098
\(302\) 0 0
\(303\) −4.16019e6 −2.60320
\(304\) 0 0
\(305\) 147347. 0.0906965
\(306\) 0 0
\(307\) −2.54290e6 −1.53987 −0.769935 0.638123i \(-0.779711\pi\)
−0.769935 + 0.638123i \(0.779711\pi\)
\(308\) 0 0
\(309\) −3.40327e6 −2.02768
\(310\) 0 0
\(311\) −2.97181e6 −1.74229 −0.871143 0.491029i \(-0.836621\pi\)
−0.871143 + 0.491029i \(0.836621\pi\)
\(312\) 0 0
\(313\) 41506.6 0.0239473 0.0119736 0.999928i \(-0.496189\pi\)
0.0119736 + 0.999928i \(0.496189\pi\)
\(314\) 0 0
\(315\) 829363. 0.470943
\(316\) 0 0
\(317\) 762636. 0.426254 0.213127 0.977024i \(-0.431635\pi\)
0.213127 + 0.977024i \(0.431635\pi\)
\(318\) 0 0
\(319\) 224841. 0.123708
\(320\) 0 0
\(321\) 5.94005e6 3.21757
\(322\) 0 0
\(323\) 1.64565e6 0.877668
\(324\) 0 0
\(325\) 239978. 0.126027
\(326\) 0 0
\(327\) 6.69615e6 3.46303
\(328\) 0 0
\(329\) 1.09166e6 0.556031
\(330\) 0 0
\(331\) −3.07851e6 −1.54444 −0.772219 0.635356i \(-0.780853\pi\)
−0.772219 + 0.635356i \(0.780853\pi\)
\(332\) 0 0
\(333\) −4.43622e6 −2.19231
\(334\) 0 0
\(335\) −801867. −0.390383
\(336\) 0 0
\(337\) 1.44180e6 0.691560 0.345780 0.938316i \(-0.387614\pi\)
0.345780 + 0.938316i \(0.387614\pi\)
\(338\) 0 0
\(339\) −1.55891e6 −0.736751
\(340\) 0 0
\(341\) −1.50172e6 −0.699364
\(342\) 0 0
\(343\) 117649. 0.0539949
\(344\) 0 0
\(345\) −1.91353e6 −0.865542
\(346\) 0 0
\(347\) −1.48182e6 −0.660649 −0.330324 0.943868i \(-0.607158\pi\)
−0.330324 + 0.943868i \(0.607158\pi\)
\(348\) 0 0
\(349\) −1.90464e6 −0.837046 −0.418523 0.908206i \(-0.637452\pi\)
−0.418523 + 0.908206i \(0.637452\pi\)
\(350\) 0 0
\(351\) 5.05491e6 2.19001
\(352\) 0 0
\(353\) −298729. −0.127597 −0.0637986 0.997963i \(-0.520322\pi\)
−0.0637986 + 0.997963i \(0.520322\pi\)
\(354\) 0 0
\(355\) −1.44980e6 −0.610573
\(356\) 0 0
\(357\) −1.17659e6 −0.488601
\(358\) 0 0
\(359\) −3.36818e6 −1.37930 −0.689651 0.724142i \(-0.742236\pi\)
−0.689651 + 0.724142i \(0.742236\pi\)
\(360\) 0 0
\(361\) 1.84523e6 0.745217
\(362\) 0 0
\(363\) 6.19327e6 2.46691
\(364\) 0 0
\(365\) 987002. 0.387780
\(366\) 0 0
\(367\) −23037.2 −0.00892820 −0.00446410 0.999990i \(-0.501421\pi\)
−0.00446410 + 0.999990i \(0.501421\pi\)
\(368\) 0 0
\(369\) −1.09643e7 −4.19196
\(370\) 0 0
\(371\) −1.28735e6 −0.485580
\(372\) 0 0
\(373\) −1.71485e6 −0.638195 −0.319097 0.947722i \(-0.603380\pi\)
−0.319097 + 0.947722i \(0.603380\pi\)
\(374\) 0 0
\(375\) 473938. 0.174038
\(376\) 0 0
\(377\) 142850. 0.0517639
\(378\) 0 0
\(379\) −1.90452e6 −0.681064 −0.340532 0.940233i \(-0.610607\pi\)
−0.340532 + 0.940233i \(0.610607\pi\)
\(380\) 0 0
\(381\) −1.07668e6 −0.379993
\(382\) 0 0
\(383\) 1.77535e6 0.618424 0.309212 0.950993i \(-0.399935\pi\)
0.309212 + 0.950993i \(0.399935\pi\)
\(384\) 0 0
\(385\) 740323. 0.254548
\(386\) 0 0
\(387\) 1.04487e7 3.54638
\(388\) 0 0
\(389\) −2.47325e6 −0.828693 −0.414346 0.910119i \(-0.635990\pi\)
−0.414346 + 0.910119i \(0.635990\pi\)
\(390\) 0 0
\(391\) 1.99766e6 0.660815
\(392\) 0 0
\(393\) 3.94911e6 1.28979
\(394\) 0 0
\(395\) −224697. −0.0724612
\(396\) 0 0
\(397\) 298950. 0.0951968 0.0475984 0.998867i \(-0.484843\pi\)
0.0475984 + 0.998867i \(0.484843\pi\)
\(398\) 0 0
\(399\) −3.08963e6 −0.971569
\(400\) 0 0
\(401\) 3.60863e6 1.12068 0.560340 0.828263i \(-0.310671\pi\)
0.560340 + 0.828263i \(0.310671\pi\)
\(402\) 0 0
\(403\) −954102. −0.292639
\(404\) 0 0
\(405\) 5.87009e6 1.77831
\(406\) 0 0
\(407\) −3.95995e6 −1.18496
\(408\) 0 0
\(409\) −431739. −0.127618 −0.0638092 0.997962i \(-0.520325\pi\)
−0.0638092 + 0.997962i \(0.520325\pi\)
\(410\) 0 0
\(411\) −7.90019e6 −2.30692
\(412\) 0 0
\(413\) 1.95358e6 0.563582
\(414\) 0 0
\(415\) −1.31309e6 −0.374260
\(416\) 0 0
\(417\) 2.76799e6 0.779514
\(418\) 0 0
\(419\) 6.10143e6 1.69784 0.848920 0.528522i \(-0.177253\pi\)
0.848920 + 0.528522i \(0.177253\pi\)
\(420\) 0 0
\(421\) 768074. 0.211202 0.105601 0.994409i \(-0.466323\pi\)
0.105601 + 0.994409i \(0.466323\pi\)
\(422\) 0 0
\(423\) 1.50835e7 4.09874
\(424\) 0 0
\(425\) −494775. −0.132873
\(426\) 0 0
\(427\) 288799. 0.0766525
\(428\) 0 0
\(429\) 7.03846e6 1.84644
\(430\) 0 0
\(431\) −1.21891e6 −0.316067 −0.158034 0.987434i \(-0.550515\pi\)
−0.158034 + 0.987434i \(0.550515\pi\)
\(432\) 0 0
\(433\) 2.44392e6 0.626423 0.313211 0.949683i \(-0.398595\pi\)
0.313211 + 0.949683i \(0.398595\pi\)
\(434\) 0 0
\(435\) 282118. 0.0714838
\(436\) 0 0
\(437\) 5.24570e6 1.31401
\(438\) 0 0
\(439\) 495858. 0.122799 0.0613997 0.998113i \(-0.480444\pi\)
0.0613997 + 0.998113i \(0.480444\pi\)
\(440\) 0 0
\(441\) 1.62555e6 0.398020
\(442\) 0 0
\(443\) 5.75805e6 1.39401 0.697006 0.717066i \(-0.254515\pi\)
0.697006 + 0.717066i \(0.254515\pi\)
\(444\) 0 0
\(445\) 1.30172e6 0.311614
\(446\) 0 0
\(447\) 1.36688e7 3.23564
\(448\) 0 0
\(449\) 4.74045e6 1.10970 0.554848 0.831952i \(-0.312777\pi\)
0.554848 + 0.831952i \(0.312777\pi\)
\(450\) 0 0
\(451\) −9.78723e6 −2.26578
\(452\) 0 0
\(453\) −9.78853e6 −2.24116
\(454\) 0 0
\(455\) 470356. 0.106512
\(456\) 0 0
\(457\) −2.61547e6 −0.585814 −0.292907 0.956141i \(-0.594623\pi\)
−0.292907 + 0.956141i \(0.594623\pi\)
\(458\) 0 0
\(459\) −1.04220e7 −2.30897
\(460\) 0 0
\(461\) −110237. −0.0241588 −0.0120794 0.999927i \(-0.503845\pi\)
−0.0120794 + 0.999927i \(0.503845\pi\)
\(462\) 0 0
\(463\) −1.53603e6 −0.333003 −0.166501 0.986041i \(-0.553247\pi\)
−0.166501 + 0.986041i \(0.553247\pi\)
\(464\) 0 0
\(465\) −1.88428e6 −0.404122
\(466\) 0 0
\(467\) 4.37245e6 0.927753 0.463877 0.885900i \(-0.346458\pi\)
0.463877 + 0.885900i \(0.346458\pi\)
\(468\) 0 0
\(469\) −1.57166e6 −0.329933
\(470\) 0 0
\(471\) −3.22610e6 −0.670078
\(472\) 0 0
\(473\) 9.32694e6 1.91684
\(474\) 0 0
\(475\) −1.29924e6 −0.264213
\(476\) 0 0
\(477\) −1.77872e7 −3.57942
\(478\) 0 0
\(479\) 2.50712e6 0.499271 0.249635 0.968340i \(-0.419689\pi\)
0.249635 + 0.968340i \(0.419689\pi\)
\(480\) 0 0
\(481\) −2.51591e6 −0.495830
\(482\) 0 0
\(483\) −3.75052e6 −0.731516
\(484\) 0 0
\(485\) 373207. 0.0720436
\(486\) 0 0
\(487\) −3.35121e6 −0.640295 −0.320147 0.947368i \(-0.603732\pi\)
−0.320147 + 0.947368i \(0.603732\pi\)
\(488\) 0 0
\(489\) −4.09211e6 −0.773882
\(490\) 0 0
\(491\) 7.04673e6 1.31912 0.659559 0.751652i \(-0.270743\pi\)
0.659559 + 0.751652i \(0.270743\pi\)
\(492\) 0 0
\(493\) −294521. −0.0545757
\(494\) 0 0
\(495\) 1.02290e7 1.87638
\(496\) 0 0
\(497\) −2.84161e6 −0.516028
\(498\) 0 0
\(499\) −8.36969e6 −1.50473 −0.752364 0.658747i \(-0.771087\pi\)
−0.752364 + 0.658747i \(0.771087\pi\)
\(500\) 0 0
\(501\) −7.05153e6 −1.25513
\(502\) 0 0
\(503\) 3.04525e6 0.536665 0.268333 0.963326i \(-0.413527\pi\)
0.268333 + 0.963326i \(0.413527\pi\)
\(504\) 0 0
\(505\) −3.42888e6 −0.598307
\(506\) 0 0
\(507\) −6.79026e6 −1.17318
\(508\) 0 0
\(509\) 564309. 0.0965434 0.0482717 0.998834i \(-0.484629\pi\)
0.0482717 + 0.998834i \(0.484629\pi\)
\(510\) 0 0
\(511\) 1.93452e6 0.327734
\(512\) 0 0
\(513\) −2.73672e7 −4.59132
\(514\) 0 0
\(515\) −2.80501e6 −0.466033
\(516\) 0 0
\(517\) 1.34641e7 2.21540
\(518\) 0 0
\(519\) −4.55436e6 −0.742180
\(520\) 0 0
\(521\) −3.99644e6 −0.645029 −0.322515 0.946564i \(-0.604528\pi\)
−0.322515 + 0.946564i \(0.604528\pi\)
\(522\) 0 0
\(523\) −4.52509e6 −0.723391 −0.361695 0.932296i \(-0.617802\pi\)
−0.361695 + 0.932296i \(0.617802\pi\)
\(524\) 0 0
\(525\) 928918. 0.147089
\(526\) 0 0
\(527\) 1.96712e6 0.308535
\(528\) 0 0
\(529\) −68550.6 −0.0106505
\(530\) 0 0
\(531\) 2.69926e7 4.15440
\(532\) 0 0
\(533\) −6.21821e6 −0.948085
\(534\) 0 0
\(535\) 4.89586e6 0.739511
\(536\) 0 0
\(537\) −1.63084e7 −2.44048
\(538\) 0 0
\(539\) 1.45103e6 0.215132
\(540\) 0 0
\(541\) −5.68445e6 −0.835018 −0.417509 0.908673i \(-0.637097\pi\)
−0.417509 + 0.908673i \(0.637097\pi\)
\(542\) 0 0
\(543\) −1.43806e7 −2.09304
\(544\) 0 0
\(545\) 5.51904e6 0.795926
\(546\) 0 0
\(547\) 7.82153e6 1.11770 0.558848 0.829270i \(-0.311244\pi\)
0.558848 + 0.829270i \(0.311244\pi\)
\(548\) 0 0
\(549\) 3.99033e6 0.565038
\(550\) 0 0
\(551\) −773389. −0.108522
\(552\) 0 0
\(553\) −440407. −0.0612409
\(554\) 0 0
\(555\) −4.96874e6 −0.684721
\(556\) 0 0
\(557\) 7.04122e6 0.961634 0.480817 0.876821i \(-0.340340\pi\)
0.480817 + 0.876821i \(0.340340\pi\)
\(558\) 0 0
\(559\) 5.92577e6 0.802076
\(560\) 0 0
\(561\) −1.45116e7 −1.94674
\(562\) 0 0
\(563\) −7.83612e6 −1.04191 −0.520955 0.853584i \(-0.674424\pi\)
−0.520955 + 0.853584i \(0.674424\pi\)
\(564\) 0 0
\(565\) −1.28487e6 −0.169331
\(566\) 0 0
\(567\) 1.15054e7 1.50295
\(568\) 0 0
\(569\) 6.57277e6 0.851075 0.425537 0.904941i \(-0.360085\pi\)
0.425537 + 0.904941i \(0.360085\pi\)
\(570\) 0 0
\(571\) −881273. −0.113115 −0.0565575 0.998399i \(-0.518012\pi\)
−0.0565575 + 0.998399i \(0.518012\pi\)
\(572\) 0 0
\(573\) −3.00670e7 −3.82563
\(574\) 0 0
\(575\) −1.57716e6 −0.198932
\(576\) 0 0
\(577\) 1.35985e7 1.70041 0.850203 0.526455i \(-0.176479\pi\)
0.850203 + 0.526455i \(0.176479\pi\)
\(578\) 0 0
\(579\) −1.20798e7 −1.49748
\(580\) 0 0
\(581\) −2.57365e6 −0.316307
\(582\) 0 0
\(583\) −1.58776e7 −1.93470
\(584\) 0 0
\(585\) 6.49890e6 0.785145
\(586\) 0 0
\(587\) −5.56764e6 −0.666923 −0.333462 0.942764i \(-0.608217\pi\)
−0.333462 + 0.942764i \(0.608217\pi\)
\(588\) 0 0
\(589\) 5.16550e6 0.613514
\(590\) 0 0
\(591\) 1.28634e7 1.51491
\(592\) 0 0
\(593\) 4.27729e6 0.499496 0.249748 0.968311i \(-0.419652\pi\)
0.249748 + 0.968311i \(0.419652\pi\)
\(594\) 0 0
\(595\) −969759. −0.112298
\(596\) 0 0
\(597\) −5.40520e6 −0.620692
\(598\) 0 0
\(599\) 6.53192e6 0.743830 0.371915 0.928267i \(-0.378701\pi\)
0.371915 + 0.928267i \(0.378701\pi\)
\(600\) 0 0
\(601\) −3.26670e6 −0.368913 −0.184456 0.982841i \(-0.559052\pi\)
−0.184456 + 0.982841i \(0.559052\pi\)
\(602\) 0 0
\(603\) −2.17156e7 −2.43208
\(604\) 0 0
\(605\) 5.10457e6 0.566984
\(606\) 0 0
\(607\) −2.17041e6 −0.239094 −0.119547 0.992829i \(-0.538144\pi\)
−0.119547 + 0.992829i \(0.538144\pi\)
\(608\) 0 0
\(609\) 552951. 0.0604148
\(610\) 0 0
\(611\) 8.55427e6 0.927001
\(612\) 0 0
\(613\) 9.89798e6 1.06389 0.531943 0.846780i \(-0.321462\pi\)
0.531943 + 0.846780i \(0.321462\pi\)
\(614\) 0 0
\(615\) −1.22805e7 −1.30927
\(616\) 0 0
\(617\) 1.68570e7 1.78266 0.891329 0.453357i \(-0.149774\pi\)
0.891329 + 0.453357i \(0.149774\pi\)
\(618\) 0 0
\(619\) 1.38025e7 1.44787 0.723935 0.689868i \(-0.242331\pi\)
0.723935 + 0.689868i \(0.242331\pi\)
\(620\) 0 0
\(621\) −3.32213e7 −3.45691
\(622\) 0 0
\(623\) 2.55137e6 0.263362
\(624\) 0 0
\(625\) 390625. 0.0400000
\(626\) 0 0
\(627\) −3.81062e7 −3.87103
\(628\) 0 0
\(629\) 5.18719e6 0.522764
\(630\) 0 0
\(631\) −9.76100e6 −0.975935 −0.487967 0.872862i \(-0.662262\pi\)
−0.487967 + 0.872862i \(0.662262\pi\)
\(632\) 0 0
\(633\) 2.53929e7 2.51886
\(634\) 0 0
\(635\) −887415. −0.0873359
\(636\) 0 0
\(637\) 921898. 0.0900191
\(638\) 0 0
\(639\) −3.92624e7 −3.80386
\(640\) 0 0
\(641\) −1.72746e7 −1.66059 −0.830295 0.557324i \(-0.811828\pi\)
−0.830295 + 0.557324i \(0.811828\pi\)
\(642\) 0 0
\(643\) −3.88097e6 −0.370180 −0.185090 0.982722i \(-0.559258\pi\)
−0.185090 + 0.982722i \(0.559258\pi\)
\(644\) 0 0
\(645\) 1.17029e7 1.10763
\(646\) 0 0
\(647\) 1.53463e7 1.44126 0.720632 0.693318i \(-0.243852\pi\)
0.720632 + 0.693318i \(0.243852\pi\)
\(648\) 0 0
\(649\) 2.40947e7 2.24548
\(650\) 0 0
\(651\) −3.69319e6 −0.341546
\(652\) 0 0
\(653\) −436146. −0.0400266 −0.0200133 0.999800i \(-0.506371\pi\)
−0.0200133 + 0.999800i \(0.506371\pi\)
\(654\) 0 0
\(655\) 3.25490e6 0.296439
\(656\) 0 0
\(657\) 2.67292e7 2.41587
\(658\) 0 0
\(659\) −6.04128e6 −0.541895 −0.270948 0.962594i \(-0.587337\pi\)
−0.270948 + 0.962594i \(0.587337\pi\)
\(660\) 0 0
\(661\) 5.67242e6 0.504969 0.252485 0.967601i \(-0.418752\pi\)
0.252485 + 0.967601i \(0.418752\pi\)
\(662\) 0 0
\(663\) −9.21977e6 −0.814584
\(664\) 0 0
\(665\) −2.54651e6 −0.223301
\(666\) 0 0
\(667\) −938823. −0.0817088
\(668\) 0 0
\(669\) −1.65557e7 −1.43015
\(670\) 0 0
\(671\) 3.56193e6 0.305407
\(672\) 0 0
\(673\) −585604. −0.0498387 −0.0249193 0.999689i \(-0.507933\pi\)
−0.0249193 + 0.999689i \(0.507933\pi\)
\(674\) 0 0
\(675\) 8.22815e6 0.695093
\(676\) 0 0
\(677\) 3.94361e6 0.330691 0.165346 0.986236i \(-0.447126\pi\)
0.165346 + 0.986236i \(0.447126\pi\)
\(678\) 0 0
\(679\) 731486. 0.0608880
\(680\) 0 0
\(681\) 3.41810e7 2.82434
\(682\) 0 0
\(683\) 1.30389e7 1.06952 0.534761 0.845003i \(-0.320402\pi\)
0.534761 + 0.845003i \(0.320402\pi\)
\(684\) 0 0
\(685\) −6.51143e6 −0.530212
\(686\) 0 0
\(687\) 4.10460e7 3.31802
\(688\) 0 0
\(689\) −1.00877e7 −0.809548
\(690\) 0 0
\(691\) 1.39341e7 1.11016 0.555079 0.831798i \(-0.312688\pi\)
0.555079 + 0.831798i \(0.312688\pi\)
\(692\) 0 0
\(693\) 2.00489e7 1.58583
\(694\) 0 0
\(695\) 2.28141e6 0.179160
\(696\) 0 0
\(697\) 1.28204e7 0.999585
\(698\) 0 0
\(699\) 3.55406e7 2.75126
\(700\) 0 0
\(701\) 2.17868e7 1.67455 0.837277 0.546779i \(-0.184146\pi\)
0.837277 + 0.546779i \(0.184146\pi\)
\(702\) 0 0
\(703\) 1.36211e7 1.03950
\(704\) 0 0
\(705\) 1.68940e7 1.28015
\(706\) 0 0
\(707\) −6.72060e6 −0.505661
\(708\) 0 0
\(709\) 9.10065e6 0.679919 0.339959 0.940440i \(-0.389587\pi\)
0.339959 + 0.940440i \(0.389587\pi\)
\(710\) 0 0
\(711\) −6.08509e6 −0.451432
\(712\) 0 0
\(713\) 6.27044e6 0.461928
\(714\) 0 0
\(715\) 5.80118e6 0.424376
\(716\) 0 0
\(717\) −4.94646e7 −3.59333
\(718\) 0 0
\(719\) 2.49384e7 1.79906 0.899532 0.436854i \(-0.143907\pi\)
0.899532 + 0.436854i \(0.143907\pi\)
\(720\) 0 0
\(721\) −5.49783e6 −0.393870
\(722\) 0 0
\(723\) −1.39522e7 −0.992655
\(724\) 0 0
\(725\) 232525. 0.0164295
\(726\) 0 0
\(727\) −2.51596e7 −1.76550 −0.882750 0.469843i \(-0.844310\pi\)
−0.882750 + 0.469843i \(0.844310\pi\)
\(728\) 0 0
\(729\) 6.19341e7 4.31629
\(730\) 0 0
\(731\) −1.22175e7 −0.845645
\(732\) 0 0
\(733\) 4.35013e6 0.299049 0.149524 0.988758i \(-0.452226\pi\)
0.149524 + 0.988758i \(0.452226\pi\)
\(734\) 0 0
\(735\) 1.82068e6 0.124313
\(736\) 0 0
\(737\) −1.93842e7 −1.31456
\(738\) 0 0
\(739\) −2.16737e7 −1.45990 −0.729948 0.683502i \(-0.760456\pi\)
−0.729948 + 0.683502i \(0.760456\pi\)
\(740\) 0 0
\(741\) −2.42103e7 −1.61978
\(742\) 0 0
\(743\) −1.05226e7 −0.699281 −0.349641 0.936884i \(-0.613696\pi\)
−0.349641 + 0.936884i \(0.613696\pi\)
\(744\) 0 0
\(745\) 1.12660e7 0.743665
\(746\) 0 0
\(747\) −3.55600e7 −2.33163
\(748\) 0 0
\(749\) 9.59588e6 0.625001
\(750\) 0 0
\(751\) 2.04846e7 1.32534 0.662670 0.748912i \(-0.269423\pi\)
0.662670 + 0.748912i \(0.269423\pi\)
\(752\) 0 0
\(753\) −795142. −0.0511042
\(754\) 0 0
\(755\) −8.06782e6 −0.515097
\(756\) 0 0
\(757\) 4.48469e6 0.284441 0.142221 0.989835i \(-0.454576\pi\)
0.142221 + 0.989835i \(0.454576\pi\)
\(758\) 0 0
\(759\) −4.62574e7 −2.91458
\(760\) 0 0
\(761\) −3.92897e6 −0.245933 −0.122967 0.992411i \(-0.539241\pi\)
−0.122967 + 0.992411i \(0.539241\pi\)
\(762\) 0 0
\(763\) 1.08173e7 0.672680
\(764\) 0 0
\(765\) −1.33991e7 −0.827795
\(766\) 0 0
\(767\) 1.53083e7 0.939590
\(768\) 0 0
\(769\) 1.23798e6 0.0754915 0.0377458 0.999287i \(-0.487982\pi\)
0.0377458 + 0.999287i \(0.487982\pi\)
\(770\) 0 0
\(771\) −3.34901e7 −2.02899
\(772\) 0 0
\(773\) −4.21618e6 −0.253788 −0.126894 0.991916i \(-0.540501\pi\)
−0.126894 + 0.991916i \(0.540501\pi\)
\(774\) 0 0
\(775\) −1.55304e6 −0.0928816
\(776\) 0 0
\(777\) −9.73872e6 −0.578695
\(778\) 0 0
\(779\) 3.36653e7 1.98765
\(780\) 0 0
\(781\) −3.50472e7 −2.05601
\(782\) 0 0
\(783\) 4.89792e6 0.285501
\(784\) 0 0
\(785\) −2.65899e6 −0.154008
\(786\) 0 0
\(787\) −2.70556e7 −1.55711 −0.778557 0.627574i \(-0.784048\pi\)
−0.778557 + 0.627574i \(0.784048\pi\)
\(788\) 0 0
\(789\) 6.66929e6 0.381406
\(790\) 0 0
\(791\) −2.51834e6 −0.143111
\(792\) 0 0
\(793\) 2.26303e6 0.127793
\(794\) 0 0
\(795\) −1.99224e7 −1.11795
\(796\) 0 0
\(797\) 2.70075e7 1.50605 0.753024 0.657993i \(-0.228594\pi\)
0.753024 + 0.657993i \(0.228594\pi\)
\(798\) 0 0
\(799\) −1.76368e7 −0.977356
\(800\) 0 0
\(801\) 3.52522e7 1.94135
\(802\) 0 0
\(803\) 2.38596e7 1.30579
\(804\) 0 0
\(805\) −3.09122e6 −0.168128
\(806\) 0 0
\(807\) 5.62139e7 3.03850
\(808\) 0 0
\(809\) −1.12425e7 −0.603937 −0.301969 0.953318i \(-0.597644\pi\)
−0.301969 + 0.953318i \(0.597644\pi\)
\(810\) 0 0
\(811\) −2.73965e7 −1.46266 −0.731331 0.682023i \(-0.761100\pi\)
−0.731331 + 0.682023i \(0.761100\pi\)
\(812\) 0 0
\(813\) 5.18326e7 2.75028
\(814\) 0 0
\(815\) −3.37276e6 −0.177865
\(816\) 0 0
\(817\) −3.20821e7 −1.68154
\(818\) 0 0
\(819\) 1.27378e7 0.663569
\(820\) 0 0
\(821\) 2.83040e7 1.46551 0.732756 0.680491i \(-0.238233\pi\)
0.732756 + 0.680491i \(0.238233\pi\)
\(822\) 0 0
\(823\) −1.63941e7 −0.843701 −0.421850 0.906665i \(-0.638619\pi\)
−0.421850 + 0.906665i \(0.638619\pi\)
\(824\) 0 0
\(825\) 1.14569e7 0.586046
\(826\) 0 0
\(827\) 3.47958e7 1.76914 0.884570 0.466407i \(-0.154452\pi\)
0.884570 + 0.466407i \(0.154452\pi\)
\(828\) 0 0
\(829\) −1.57884e7 −0.797905 −0.398952 0.916972i \(-0.630626\pi\)
−0.398952 + 0.916972i \(0.630626\pi\)
\(830\) 0 0
\(831\) 5.72828e6 0.287754
\(832\) 0 0
\(833\) −1.90073e6 −0.0949090
\(834\) 0 0
\(835\) −5.81196e6 −0.288474
\(836\) 0 0
\(837\) −3.27134e7 −1.61403
\(838\) 0 0
\(839\) −1.22890e7 −0.602714 −0.301357 0.953511i \(-0.597440\pi\)
−0.301357 + 0.953511i \(0.597440\pi\)
\(840\) 0 0
\(841\) −2.03727e7 −0.993252
\(842\) 0 0
\(843\) 5.38292e7 2.60885
\(844\) 0 0
\(845\) −5.59661e6 −0.269639
\(846\) 0 0
\(847\) 1.00050e7 0.479189
\(848\) 0 0
\(849\) 1.43214e7 0.681895
\(850\) 0 0
\(851\) 1.65348e7 0.782664
\(852\) 0 0
\(853\) 3.39815e7 1.59908 0.799539 0.600615i \(-0.205077\pi\)
0.799539 + 0.600615i \(0.205077\pi\)
\(854\) 0 0
\(855\) −3.51850e7 −1.64605
\(856\) 0 0
\(857\) 7.74121e6 0.360045 0.180022 0.983662i \(-0.442383\pi\)
0.180022 + 0.983662i \(0.442383\pi\)
\(858\) 0 0
\(859\) −3.03603e7 −1.40386 −0.701930 0.712246i \(-0.747678\pi\)
−0.701930 + 0.712246i \(0.747678\pi\)
\(860\) 0 0
\(861\) −2.40697e7 −1.10653
\(862\) 0 0
\(863\) −3.02445e7 −1.38235 −0.691177 0.722686i \(-0.742907\pi\)
−0.691177 + 0.722686i \(0.742907\pi\)
\(864\) 0 0
\(865\) −3.75376e6 −0.170579
\(866\) 0 0
\(867\) −2.40582e7 −1.08697
\(868\) 0 0
\(869\) −5.43180e6 −0.244002
\(870\) 0 0
\(871\) −1.23155e7 −0.550057
\(872\) 0 0
\(873\) 1.01069e7 0.448831
\(874\) 0 0
\(875\) 765625. 0.0338062
\(876\) 0 0
\(877\) 2.48236e7 1.08985 0.544924 0.838485i \(-0.316558\pi\)
0.544924 + 0.838485i \(0.316558\pi\)
\(878\) 0 0
\(879\) −1.94768e7 −0.850246
\(880\) 0 0
\(881\) 4.40667e7 1.91281 0.956403 0.292050i \(-0.0943374\pi\)
0.956403 + 0.292050i \(0.0943374\pi\)
\(882\) 0 0
\(883\) −3.46407e6 −0.149515 −0.0747574 0.997202i \(-0.523818\pi\)
−0.0747574 + 0.997202i \(0.523818\pi\)
\(884\) 0 0
\(885\) 3.02327e7 1.29754
\(886\) 0 0
\(887\) 1.67314e7 0.714039 0.357020 0.934097i \(-0.383793\pi\)
0.357020 + 0.934097i \(0.383793\pi\)
\(888\) 0 0
\(889\) −1.73933e6 −0.0738123
\(890\) 0 0
\(891\) 1.41903e8 5.98820
\(892\) 0 0
\(893\) −4.63128e7 −1.94345
\(894\) 0 0
\(895\) −1.34416e7 −0.560909
\(896\) 0 0
\(897\) −2.93891e7 −1.21957
\(898\) 0 0
\(899\) −924470. −0.0381499
\(900\) 0 0
\(901\) 2.07983e7 0.853523
\(902\) 0 0
\(903\) 2.29378e7 0.936121
\(904\) 0 0
\(905\) −1.18526e7 −0.481054
\(906\) 0 0
\(907\) 1.76952e7 0.714227 0.357114 0.934061i \(-0.383761\pi\)
0.357114 + 0.934061i \(0.383761\pi\)
\(908\) 0 0
\(909\) −9.28583e7 −3.72744
\(910\) 0 0
\(911\) 4.39235e6 0.175348 0.0876740 0.996149i \(-0.472057\pi\)
0.0876740 + 0.996149i \(0.472057\pi\)
\(912\) 0 0
\(913\) −3.17423e7 −1.26026
\(914\) 0 0
\(915\) 4.46932e6 0.176477
\(916\) 0 0
\(917\) 6.37961e6 0.250536
\(918\) 0 0
\(919\) 2.35758e7 0.920825 0.460412 0.887705i \(-0.347702\pi\)
0.460412 + 0.887705i \(0.347702\pi\)
\(920\) 0 0
\(921\) −7.71314e7 −2.99628
\(922\) 0 0
\(923\) −2.22669e7 −0.860310
\(924\) 0 0
\(925\) −4.09529e6 −0.157373
\(926\) 0 0
\(927\) −7.59633e7 −2.90338
\(928\) 0 0
\(929\) 2.38326e7 0.906007 0.453004 0.891509i \(-0.350352\pi\)
0.453004 + 0.891509i \(0.350352\pi\)
\(930\) 0 0
\(931\) −4.99115e6 −0.188724
\(932\) 0 0
\(933\) −9.01409e7 −3.39014
\(934\) 0 0
\(935\) −1.19606e7 −0.447429
\(936\) 0 0
\(937\) 2.52434e6 0.0939288 0.0469644 0.998897i \(-0.485045\pi\)
0.0469644 + 0.998897i \(0.485045\pi\)
\(938\) 0 0
\(939\) 1.25898e6 0.0465966
\(940\) 0 0
\(941\) 3.95629e7 1.45651 0.728257 0.685305i \(-0.240331\pi\)
0.728257 + 0.685305i \(0.240331\pi\)
\(942\) 0 0
\(943\) 4.08666e7 1.49654
\(944\) 0 0
\(945\) 1.61272e7 0.587461
\(946\) 0 0
\(947\) −1.96005e7 −0.710218 −0.355109 0.934825i \(-0.615556\pi\)
−0.355109 + 0.934825i \(0.615556\pi\)
\(948\) 0 0
\(949\) 1.51589e7 0.546391
\(950\) 0 0
\(951\) 2.31323e7 0.829406
\(952\) 0 0
\(953\) 1.69856e7 0.605828 0.302914 0.953018i \(-0.402041\pi\)
0.302914 + 0.953018i \(0.402041\pi\)
\(954\) 0 0
\(955\) −2.47815e7 −0.879265
\(956\) 0 0
\(957\) 6.81987e6 0.240711
\(958\) 0 0
\(959\) −1.27624e7 −0.448111
\(960\) 0 0
\(961\) −2.24546e7 −0.784325
\(962\) 0 0
\(963\) 1.32586e8 4.60715
\(964\) 0 0
\(965\) −9.95629e6 −0.344175
\(966\) 0 0
\(967\) 1.70160e7 0.585184 0.292592 0.956237i \(-0.405482\pi\)
0.292592 + 0.956237i \(0.405482\pi\)
\(968\) 0 0
\(969\) 4.99158e7 1.70777
\(970\) 0 0
\(971\) −1.53215e7 −0.521499 −0.260750 0.965406i \(-0.583970\pi\)
−0.260750 + 0.965406i \(0.583970\pi\)
\(972\) 0 0
\(973\) 4.47156e6 0.151418
\(974\) 0 0
\(975\) 7.27901e6 0.245223
\(976\) 0 0
\(977\) 1.60455e7 0.537795 0.268898 0.963169i \(-0.413341\pi\)
0.268898 + 0.963169i \(0.413341\pi\)
\(978\) 0 0
\(979\) 3.14675e7 1.04931
\(980\) 0 0
\(981\) 1.49463e8 4.95861
\(982\) 0 0
\(983\) 4.45298e7 1.46983 0.734914 0.678160i \(-0.237222\pi\)
0.734914 + 0.678160i \(0.237222\pi\)
\(984\) 0 0
\(985\) 1.06021e7 0.348180
\(986\) 0 0
\(987\) 3.31123e7 1.08192
\(988\) 0 0
\(989\) −3.89447e7 −1.26607
\(990\) 0 0
\(991\) −9.31862e6 −0.301417 −0.150708 0.988578i \(-0.548155\pi\)
−0.150708 + 0.988578i \(0.548155\pi\)
\(992\) 0 0
\(993\) −9.33774e7 −3.00517
\(994\) 0 0
\(995\) −4.45503e6 −0.142657
\(996\) 0 0
\(997\) −4.78418e7 −1.52430 −0.762149 0.647402i \(-0.775856\pi\)
−0.762149 + 0.647402i \(0.775856\pi\)
\(998\) 0 0
\(999\) −8.62634e7 −2.73472
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 280.6.a.j.1.5 5
4.3 odd 2 560.6.a.y.1.1 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
280.6.a.j.1.5 5 1.1 even 1 trivial
560.6.a.y.1.1 5 4.3 odd 2